Objective: How to create a linear equation given two points on a graph.


Creator: Ms. Blasioli


Explanation: First you must find the slope using the two points external image mimetex.cgi?%28x_%7B1%7D,%5C%20y_%7B1%7D%29%5C%20and%20%5C%20%28x_%7B2%7D,%5C%20y_%7B2%7D%29and the slope formula external image mimetex.cgi?slope%5C%20=%5Cfrac%20%7By_%7B1%7D-y_2%7D%7Bx_%7B1%7D-x_%7B2%7D%7D.

Once you determine the slope, you can now substitute into the slope-intercept form of a linear equation external image mimetex.cgi?y=mx+b. Substitute in the slope for m, and then sub in the external image mimetex.cgi?x_%7B1%7Dvalue for the external image mimetex.cgi?xand the external image mimetex.cgi?y_%7B1%7Dvalue for the external image mimetex.cgi?y. You are now ready to solve for the external image mimetex.cgi?bin the slope-intercept equation. This will give you the y-intercept. When you have the y-intercept and the slope, then you can write the equation in the slope intercept form.




Sample: Given (4, 5) and (8, 3), write the linear equation that passes through these two points. First find the slope:

external image mimetex.cgi?slope%20=%20%5C%20%5Cfrac%20%7B4-8%7D%7B5-3%7D%20%5C%5C%20slope%20=%20%5C%20%5Cfrac%20%7B-4%7D%7B2%7D%20%5C%5C%20slope%20=%20-2

Use the 1st order pair (4,5) and substitute in 4 for x, 5 for y and -2 for m and find the b (the y-intercept).

external image mimetex.cgi?5=4%28-2%29+b%20%5C%5C%205=-8+b%20%5C%20%28add%5C%208%20%5C%20to%5C%20both%20%5C%20sides%29%5C%5C%20%2013=b

Finally, write the equation of the line passing through points (4, 5) and (8, 3). The equation in slope-intercept form is external image mimetex.cgi?y=-2x+13


external image mimetex.cgi?y=4x%5E2